On a Hardy-Type Integral Inequality under Convexity and Submultiplicativity Assumptions

Christophe Chesneau

On a Hardy-Type Integral Inequality under Convexity and Submultiplicativity Assumptions

Abstract

The focus of this article is a Hardy-type integral inequality published in 2012, which has the particularity of combining convexity and submultiplicativity assumptions. A revision is carried out in several steps. First, a counterexample to this result is given, questioning its validity. Then an alternative statement is proposed, together with a detailed proof. Among the facts revealed is the relaxation of the assumption on a key parameter of the integral norm. Finally, several examples of the revised result are presented, showing a new modification of the Hardy integral inequality. Their originality takes advantage of the combined convexity and submultiplicativity assumptions, which remain an underexplored framework.

Keywords

References

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Details

Primary Language

English

Subjects

Mathematical Methods and Special Functions

Journal Section

Research Article

Authors

Christophe Chesneau ^*
France

Early Pub Date

April 29, 2025

Publication Date

April 30, 2025

Submission Date

December 15, 2024

Acceptance Date

April 7, 2025

Published in Issue

Year 2025 Volume: 13 Number: 1

IZ

https://izlik.org/JA92HZ28UU

Cite

RIS / Bibtex

APA

Chesneau, C. (2025). On a Hardy-Type Integral Inequality under Convexity and Submultiplicativity Assumptions. Konuralp Journal of Mathematics, 13(1), 87-92. https://izlik.org/JA92HZ28UU

AMA

1.Chesneau C. On a Hardy-Type Integral Inequality under Convexity and Submultiplicativity Assumptions. Konuralp J. Math. 2025;13(1):87-92. https://izlik.org/JA92HZ28UU

Chicago

Chesneau, Christophe. 2025. “On a Hardy-Type Integral Inequality under Convexity and Submultiplicativity Assumptions”. Konuralp Journal of Mathematics 13 (1): 87-92. https://izlik.org/JA92HZ28UU.

EndNote

Chesneau C (April 1, 2025) On a Hardy-Type Integral Inequality under Convexity and Submultiplicativity Assumptions. Konuralp Journal of Mathematics 13 1 87–92.

IEEE

[1]C. Chesneau, “On a Hardy-Type Integral Inequality under Convexity and Submultiplicativity Assumptions”, Konuralp J. Math., vol. 13, no. 1, pp. 87–92, Apr. 2025, [Online]. Available: https://izlik.org/JA92HZ28UU

ISNAD

Chesneau, Christophe. “On a Hardy-Type Integral Inequality under Convexity and Submultiplicativity Assumptions”. Konuralp Journal of Mathematics 13/1 (April 1, 2025): 87-92. https://izlik.org/JA92HZ28UU.

JAMA

1.Chesneau C. On a Hardy-Type Integral Inequality under Convexity and Submultiplicativity Assumptions. Konuralp J. Math. 2025;13:87–92.

MLA

Chesneau, Christophe. “On a Hardy-Type Integral Inequality under Convexity and Submultiplicativity Assumptions”. Konuralp Journal of Mathematics, vol. 13, no. 1, Apr. 2025, pp. 87-92, https://izlik.org/JA92HZ28UU.

Vancouver

1.Christophe Chesneau. On a Hardy-Type Integral Inequality under Convexity and Submultiplicativity Assumptions. Konuralp J. Math. [Internet]. 2025 Apr. 1;13(1):87-92. Available from: https://izlik.org/JA92HZ28UU